Perhaps the most pressing industrial and technological need for improvement in quantum scale modeling of molecules and molecular materials is to develop new methods and algorithms that deliver improved accuracy at reduced computational cost. Specifically, today's best methods involve computational cost that increases by a factor of 128 when the molecule size increases by a factor of 2. Furthermore even their robustness is questionable under some conditions. This proposal seeks to combine three important elements to remedy the current situation. These elements are first, an improved basic method, second, a reduced scaling implementation of the method, and third, exploitation of massively parallel computing power. PROPOSED COMMERCIAL APPLICATIONS: The Phase I research plan is designed to demonstrate the feasibility of the concept, by showing improved accuracy on model problems relevant to industry, and illustrating substantially improved scaling of computation with molecular size, without significant loss of numerical precision.